The first thing you want to do is perform an update on your DSTWO with a DS Phat or DS Lite. Extract the contents from this ZIP onto the root directory of your MicroSD. Drop the contents of this onto the MicroSD root directory as well.

You should have these files on your MicroSD card:
SD:/_dstwo/
SD:/dstwoupdate.dat
SD:/ds2boot.dat

Run your flashcart on a DS Phat/DS Lite and it should prompt you to update, which you should do. When it's done power off.
Put the flashcart in your 3DS. Look at the game logo before running it. Make sure you get this logo:

If you do, rename dstwoupdate.dat to dstwoupdateb.dat, then run the card on the 3DS.

You will get an error message:
Don't let this scare you, though. Sit on that error screen for at least three (3) minutes. Once the 3+ minutes are up, shut off the 3DS, delete dstwoupdateb.dat, and your flashcart should run fine at this point.